I watch Islamic videos on the Internet, I really enjoy them and I have learnt a lot from them. I am not sure if the people who uploaded these videos online got permission from the speakers. They are mostly Islam related dawah videos so I guess it's no harm of downloading them but I am not sure. I don't want to do anything haram so do you need permission to download Islamic videos from speakers themselves?
You need to check whether the content has a copy-right or not first.
Basically in Islam anybody is required to share his knowledge and spread it. Therefore in Islamic jurisprudence the matter of copy-right is somewhat discussed as in general there's no "copy-right" on knowledge, scholars may discuss what "knowledge" refers to? Knowledge in general? only religious knowledge? etc.. But if in the material you copy or download there's an information telling you that this has a copy-right you are hold on or recommended (depending on the scholarly opinion) to legally buy it as Muslims are hold on to fulfill contracts based on (5:1).
So if you know that usually lectures from a certain scholar are not available for free you should have in mind that you might be acting against the later verse if you downloaded them.